In the framework of array measurements of ambient vibrations, the objective of this thesis was to improve the inversion of dispersion curves in order to retrieve the 
profile of a ground structure. The uncertainties in the determination of the dispersion curve generally lead to a problem highly affected by non-uniqueness. Direct search methods, like the neighbourhood algorithm considered in this work, offer at least two advantages over classical linearization approaches: the whole parameter space is investigated and prior information is easily introduced by restricting the search to particular regions of the parameter space. However, these methods require a great number of forward computations. Moreover, the calculation of theoretical dispersion curves is done numerically and classical codes need to be tuned on a case-by-base basis to give the right answer. Consequently, we developed a new optimized and reliable algorithm to calculate the theoretical dispersion curve of any one-dimensional model, including fundamental and higher modes of Rayleigh and Love waves. We also extended the capabilities of the tool to the inversion of the auto-correlation curves.
The Rayleigh dispersion curves observed on the vertical components are generally not available at low frequency due to the high-pass filter effect of the ground structure, which drastically reduces the penetration depth of the method. A variety of strategies were tested to overcome this limitation. The contribution of prior information about 
, about the depth of the major contrasts, and about the frequency of the H/V peak were considered. No significant improvement was found with only one of these types of additional constraints, but their combined effects always help in a better definition of the
profile.
Configurations with a great number of layers, ten in our case, showed that the non-uniqueness of the problem dramatically increases when low velocity zones are allowed in the ground model. However, forbidding such model feature is not straightforward with the original neighbourhood code. Several strategies were developed which prove that this kind of prior information is of prime importance. The lack of flexibility with these approaches led us to revise the neighbourhood algorithm itself. It was re-written in C++ with the possibility of fixing prior conditions between parameters, like the one induced by Poisson's ratio or by the absence of negative velocity contrast. This alternative offers good perspectives, eventually for other purposes, but intensive testing is still necessary.
The horizontal components are usually high-pass filtered at a lower frequency than the vertical ones. If the dispersion curve of Love waves can be estimated, the joint inversion of high frequency Rayleigh and low frequency Love dispersion curves is a good alternative to investigate the deep part of the ground model. This is an interesting property that opens perspectives towards a better prediction of the site amplification from array measurements.
The observed dispersion curves might follow the fundamental (usual assumption) or any of the higher modes. If the harmonic branches can be correctly identified, including all modes into the inversion slightly improves the final results. It also provides a good way of confirming the inversion results obtained with the fundamental mode. However, for our test case, the frequency range where the first higher mode is likely to be observed contains redundant information with the fundamental mode. On the contrary, we show that a misidentification of the observed modes introduces bias in the results. An experimental code is developed to search all possible solutions not requiring a preliminary and subjective identification of the modes. Assuming the number of potential modes, we show that only a few model classes really fit the data curve. Prior information is still necessary to select the appropriate family of models.
We tested the inversion tool for non-perfect dispersion curves estimated from microtremor recordings, either synthetic or real. Signal processing of array measurements includes the frequency-wavenumber, the high resolution frequency-wavenumber, and the auto-correlation methods. These methods provide a reliable dispersion curve over a limited wavenumber range which mainly depends upon the array geometry. Including biased part of the curves into the inversion might lead to incorrect results. Hence, strict rules for pre-processing input curves are developed. We tested the relevance of the limits deduced from the theoretical array response which is entirely calculated with the array geometry. A good agreement is found between them and the range of the correct determination of the dispersion curve.
Among the methods for processing the raw recordings of ambient vibrations, the auto-correlation method does not provide the dispersion curve in a direct way like the frequency-wavenumber methods. Classical approaches involve two inversion processes which are known to be highly non-linear. We developed a one step inversion with the neighbourhood algorithm. Besides the simplicity, the advantage of this method is that the auto-correlation data uncertainties are fully considered during the inversion. An original contribution of this work is also the definition of a methodology for assessing the valuable parts of the auto-correlation curves to invert.
The alluvial plain of Meuse river (Liège, Belgium) has been choosen for the deployement of the array method due to its one-dimensional structure (shallow alluvial deposits overlying a shaly bed-rock) and due to the available geotechnical data. Information from boreholes, classical refraction, active surface wave experiments, and from the H/V peak frequency were analysed to check the validity of the array results. Only the frequency-wavenumber method provided consistent dispersion curves for all arrays and proved to be the most robust. The results of the high resolution technique globally agreed with the first method but exhibit unexpected sharp variations of the dispersion curve at some frequencies. Finally, the auto-correlation technique was only usable for one array. These last two methods appeared to be very sensitive to uncorrelated noise. A reliable
profile was obtained down to 10 m. The depth of the main velocity contrast is estimated with a relatively good precision (the depths found vary from 9 to 14 m) but no information can be retrieved below. This reinforces the interest of investigating the three-components techniques to retrieve the Love dispersion curve.
During this thesis, we developed a collection of interpretation techniques devoted to ambient vibration measurements. Prior information is necessary to overcome the non-uniqueness of the dispersion curve inversion. We provided the tool for integrating them in a rational way.
Several promising improvements have still to be studied and tested. The extraction of Love dispersion curve from ambient vibrations is not as direct as the determination of Rayleigh dispersion curve from the vertical component. Signal processing methods have to be tested on synthetic and real experiments to assess the real potentialities. The spatial auto-correlation method applied on the three components of the recordings also offers a solution to characterize the relative portions of Love and Rayleigh waves in microtremors, which is a necessary step for understanding the noise wavefield structure.
The conditional neighbourhood algorithm developed in this thesis takes into account the physical conditions between parameters, which is necessary to avoid the low velocity zones during inversion. This work proved that this kind of prior information is of prime importance. However, this code still needs intensive testing.
The use of a resampling of the ensemble of models (Sambridge (1999b)) may provide objective statistics that are not possible with the current misfit based approach.
The joint inversion with refraction measurements and a better recognition of the higher modes by means of external information are also topics to study in order to improve the velocity accuracy.
All the preceding discussion focalized on one-dimensional models. Extension to three-dimensional cases might be considered in the future with the current development of finite difference codes to simulate the ambient vibrations. If the direct inversion is still not considered with these codes, currently available three-dimensional synthetic wavefields will give the opportunity of a better understanding of the noise properties in such cases.